Calculations of horizontal displacements due to a rectangular finite thrust fault in a viscoelastic-gravitational layered Earth model are presented. The Earth model consists of a single elastic-gravitational layer overlying a viscoelastic-gravitational half-space. A review of the full three-dimensional theoretical solutions is presented along with the explicit solutions for horizontal displacements. Several examples of computations for dipping faults with various angles, and located at different depths, are shown. The results indicate that viscoelasticity introduces a long-wavelength component into the interseismic deformation field which is not present in published elastic techniques and also that a proper consideration of gravity is necessary only for near-field computations at longer periods of time. A pattern is found in the cumulative displacement of cycled earthquakes, which indicates that the viscoelastic displacements are visible for longer recurrence time events and that these may serve as a time index for the various stages between cycles. ¿ American Geophysical Union 1996